Rewrite as a simplified fraction. ${0.8\overline{86} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 886.8686...\\ 10x &= 8.8686...\end{align*}}$ Subtracting the two equations, we have: ${990x = 878}$ ${x = \dfrac{878}{990}} $ ${x = \dfrac{439}{495}} $